Humanity's love affair with mathematics and mysticism reached a critical juncture, legend has it, on the back of a turtle in ancient China. As Clifford Pickover briefly recounts in this enthralling book, the most comprehensive in decades on magic squares, Emperor Yu was supposedly strolling along the Yellow River one day around 2200 B.C. when he spotted the creature: its shell had a series of dots within squares. To Yu's amazement, each row of squares contained fifteen dots, as did the columns and diagonals. When he added any two cells opposite along a line through the center square, like 2 and 8, he always arrived at 10. The turtle, unwitting inspirer of the ""Yu"" square, went on to a life of courtly comfort and fame. Pickover explains why Chinese emperors, Babylonian astrologer-priests, prehistoric cave people in France, and ancient Mayans of the Yucatan were convinced that magic squares--arrays filled with numbers or letters in certain arrangements--held the secret of the universe. Since the dawn of civilization, he writes, humans have invoked such patterns to ward off evil and bring good fortune.
Yet who would have guessed that in the twenty-first century, mathematicians would be studying magic squares so immense and in so many dimensions that the objects defy ordinary human contemplation and visualization?
Readers are treated to a colorful history of magic squares and similar structures, their construction, and classification along with a remarkable variety of newly discovered objects ranging from ornate inlaid magic cubes to hypercubes. Illustrated examples occur throughout, with some patterns from the author's own experiments. The tesseracts, circles, spheres, and stars that he presents perfectly convey the age-old devotion of the math-minded to this Zenlike quest. Number lovers, puzzle aficionados, and math enthusiasts will treasure this rich and lively encyclopedia of one of the few areas of mathematics where the contributions of even nonspecialists count.
By:
Clifford A. Pickover
Imprint: Princeton University Pres
Country of Publication: United States
Edition: New edition
Dimensions:
Height: 235mm,
Width: 152mm,
Spine: 24mm
Weight: 624g
ISBN: 9780691115979
ISBN 10: 0691115974
Pages: 432
Publication Date: 30 March 2004
Audience:
General/trade
,
College/higher education
,
Professional and scholarly
,
ELT Advanced
,
Primary
Format: Paperback
Publisher's Status: Active
Preface xi Acknowledgments xix Introduction 1 CHAPTER ONE: Magic Construction 37 CHAPTER TWO: Classification 65 CHAPTER THREE: Gallery I : Squares, Cubes, and Tesseracts 147 CHAPTER FOUR: Gallery 2: Circles and Spheres 297 CHAPTER FIVE: Gallery 3: Stars, Hexagons, and Other Beauties 325 Some Final Thoughts 369 Notes 375 For Further Reading 395 Index 397 About the Author 403
Clifford Pickover is the author of over twenty books on a broad range of topics in science and art, a columnist for Odyssey , and an inventor. His books include Surfing Through Hyperspace: Understanding Higher Universes in Six Easy Lessons, Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning, and The Loom of God: Mathematical Tapestries at the Edge of Time .
Reviews for The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions
A perpetual idea machine, Clifford Pickover is one of the most creative, original thinkers in the world today. --Journal of Recreational Mathematics Pickover just seems to exist in more dimensions than the rest of us. --Ian Stewart, Scientific American Clifford Pickover is many things--scientist, scholar, author, editor, and visionary... --Games It is a safe bet to conjecture that this is the best recreational mathematics book that will be published in this year... Pickover writes with his usual style and straightforward simplicity in this book. The material is presented well and can be understood by anyone with a basic middle school mathematics background. This is a cool book! --Charles Ashbacker, Journal of Recreational Mathematics Through accessible and readable prose and through detailed, highquality line illustrations, Pickover ably transports the general reader from culturally embedded traditional topics to a new and surprising frontier. --Harold Don Allen, Mathematics Teacher Pickover writes about his subject with contagious enthusiasm and comprehensive erudition. --Choice A splendid recreational book... An extremely alluring page-turner. --Andrew Bremner, Notices of the American Mathematical Society
